Difference between revisions of "Publications/boutry.20.jmiv.1"
From LRDE
Line 19: | Line 19: | ||
author = <nowiki>{</nowiki>Nicolas Boutry and Laurent Najman and Thierry G\'eraud<nowiki>}</nowiki>, |
author = <nowiki>{</nowiki>Nicolas Boutry and Laurent Najman and Thierry G\'eraud<nowiki>}</nowiki>, |
||
title = <nowiki>{</nowiki>Topological Properties of the First Non-Local Digitally |
title = <nowiki>{</nowiki>Topological Properties of the First Non-Local Digitally |
||
− | Well-Composed Interpolation on $n$-D Cubical Grids<nowiki>}</nowiki>, |
+ | Well-Composed Interpolation on <nowiki>{</nowiki>$n$-D<nowiki>}</nowiki> Cubical Grids<nowiki>}</nowiki>, |
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>, |
||
volume = <nowiki>{</nowiki>62<nowiki>}</nowiki>, |
volume = <nowiki>{</nowiki>62<nowiki>}</nowiki>, |
Revision as of 09:57, 5 November 2020
- Authors
- Nicolas Boutry, Laurent Najman, Thierry Géraud
- Journal
- Journal of Mathematical Imaging and Vision
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2020-09-03
Abstract
In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in -D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an -D interpolation which is at the same time localself-dual, and well-composed. By removing the locality constraint, we have obtained an -D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given.
Documents
Bibtex (lrde.bib)
@Article{ boutry.20.jmiv.1, author = {Nicolas Boutry and Laurent Najman and Thierry G\'eraud}, title = {Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on {$n$-D} Cubical Grids}, journal = {Journal of Mathematical Imaging and Vision}, volume = {62}, number = {}, pages = {1256--1284}, month = sep, year = {2020}, abstract = {In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in $n$-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However, it has been proved that we cannot have an $n$-D interpolation which is at the same time local, self-dual, and well-composed. By removing the locality constraint, we have obtained an $n$-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given. } }